A decoupled, convergent and fully linear algorithm for the Landau-Lifshitz-Gilbert equation with magnetoelastic effects

Abstract: The mechanical and magnetic properties of ferromagnetic materials are strongly coupled. Applying a stress to a ferromagnetic material changes the magnetic state, and applying a magnetic field deforms it. These fall collectively under the phenomena of "magnetostriction". We consider the coupled system of the Landau-Lifshitz-Gilbert (LLG) equation and conservation of momentum to describe magnetostrictive processes. For this nonlinear system of time-dependent partial differential equations, we present a decoupled and unconditionally convergent integrator based on linear finite elements in space and a one-step method in time. Compared to previous works on this problem, for our method, we prove a discrete energy law that mimics that of the continuous problem. Moreover, we do not employ a nodal projection to impose the unit-length constraint on the discrete magnetization, so that the stability of the method does not require weakly acute meshes. Furthermore, our integrator and its analysis hold for a more general setting, including body forces and traction, and a more general representation of the magnetostrain.

H. Normington and M. Ruggeri, A decoupled, convergent and fully linear algorithm for the Landau--Lifshitz--Gilbert equation with magnetoelastic effects. (under review), arxiv.org/abs/2309.00605v2

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)